It looks like you've uploaded an image with some logic homework problems. The task involves proving logical equivalences and writing truth tables for the following logical statements:

1. (a) $P \leftrightarrow Q$ ⇔ $\neg P \leftrightarrow \neg Q$
2. (b) $P \vee (Q \leftrightarrow R)$ ⇔ $(P \vee Q) \leftrightarrow (P \vee R)$
3. (c) $P \land (Q \leftrightarrow \neg P)$ ⇔ $(P \vee Q)$
4. (d) $P \vee Q \land (R \leftrightarrow P)$ ⇔ $(P \vee Q)$

To solve this, we will need to work through each statement step by step, proving the equivalence using truth tables and logical rules.

Would you like me to go over each of these problems with detailed explanations?